... yes? I still hear a 440 and a 450 tone together? It is hard to discriminate what the frequency of the highest note is, however, because of an effect called masking in the frequency domain which is a psychoacoustic effect, quite different from the "beating" effect what you were talking about earlier.

I'm sorry, I hear the base frequency above 440 Hz.

Ok. It is important to notice that all changes in frequency in this case happen in your ears and brains not in the recording or playback process.

QUOTE

I may take that back, however. I may keep with the beat, only.

By now, do you believe me if I say that the "beat" is just a change in amplitude? And that we can only hear a tone "beat" if we can also hear the tone without the beating, i.e. if the frequency of the original tone is in the hearable range?

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QUOTE (bug80 @ Feb 9 2006, 07:16 PM)

QUOTE (hdante @ Feb 9 2006, 09:09 PM)

I meant listen to it. Listen to a 440 Hz tone, listen to a 445 tone, listen to a 450 tone, an then listen to a 440+450 tone.

... yes? I still hear a 440 and a 450 tone together?

I dont, I hear a single wowowowowowing tone. SebG formulated this should be 445 Hz, amplitude modulated sinusoidaly at 5Hz, which is ten wobbles -or semicycles, a second.

I think if you listen to progressively further apart tones, the wobbling becomes faster until its not perceived any more, that should be the change from hearing one beating tone to hearing two non interfering tones. As you move them closer - especialy while tuning guitar eg, you mostly hear one tone (main note +guitar overtones) that is increasing and decreasing in loudness - once a second or longer, keep tuning closer and closer until finaly the notes are close enough for them to properly resonate with each other through the body, and your in tune (the strings then sustain for much longer).

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QUOTE (bug80 @ Feb 9 2006, 07:45 PM)

QUOTE (ChiGung @ Feb 9 2006, 09:40 PM)

QUOTE (bug80 @ Feb 9 2006, 07:16 PM)

QUOTE (hdante @ Feb 9 2006, 09:09 PM)

I meant listen to it. Listen to a 440 Hz tone, listen to a 445 tone, listen to a 450 tone, an then listen to a 440+450 tone.

... yes? I still hear a 440 and a 450 tone together?

I dont, I hear a single wowowowowowing tone. SebG formulated this should be 445 Hz, amplitude modulated sinusoidaly at 5Hz, which is ten wobbles -or semicycles, a second.

I only hear one tone if the difference is lower, say 445 and 450 Hz. Again, this is all perception, we hear two tones but we perceive them as one wobbling tone.

Does it follow we could be subjected to one wobbling tone and percieve it as two?How could we know the difference if there were two beatles singing mating tones to each other, or one strange wobbling beatle all on its own

It's a matter of time/frequency resolution. If you do a short-window FFT on two closely spaced (in frequency domain) sines you'll see one wobbeling sine. With a long analysis window, you'll see 2 constant sines.

By now, do you believe me if I say that the "beat" is just a change in amplitude? And that we can only hear a tone "beat" if we can also hear the tone without the beating, i.e. if the frequency of the original tone is in the hearable range?

I surely believe you when you say the beat is just a change in amplitude. And the requirement of the original tone is reasonable. But, as I say, I couldn't hear the original 440 Hz tone. It would be really nice if there's research on that. I think there's no more of this to be discussed (it's getting boring, ain't it ?).

By now, do you believe me if I say that the "beat" is just a change in amplitude? And that we can only hear a tone "beat" if we can also hear the tone without the beating, i.e. if the frequency of the original tone is in the hearable range?

I surely believe you when you say the beat is just a change in amplitude. And the requirement of the original tone is reasonable. But, as I say, I couldn't hear the original 440 Hz tone. It would be really nice if there's research on that.

There's lots of research on that. Just google on 'psychoacoustics' and you will find lots of information. For example:

There's too much interpreting here. I've found a "third-party" argument which mirrors my original statement and I hope it is pretty understandable. However, I insist that the 2 KHz was wrong and 1 KHz would be the correct result (there's the same error in the quote that follows).

QUOTE (mika @ music player)

(...)[...]Theoretically, if we put two oscillators in a room - one at 30k and one at 45k, a microphone would pick up a 15k harmonic that we could hear. If we had the same oscillators in different rooms and recorded them both at 44.1k and mixed them we would not hear this phenomena. If, however, we recorded them at 96k (assuming the filters on the converters rolled off at 48k and not earlier) and mixed them we would once again hear this 15k overtone. This is supposedly an example of where recording and mixing at 96k can achieve different sonic characteristics even if the recording was to be reproduced on a 48k medium. The overtones discussed above would be produced in the mixing process and would endure the downsampling process.[...]

This guy seems to be agreeing with my opinion on this, except for the last point about reproducing on a 48k medium. From my experiments when you downsample to 48k or 44.1k the 'ultrasonic' tones disappear and the beat frequency disappears with it (as you'd expect)! So unless mastering engineers start making 44.1khz masters by going 96k > analog > 44.1k it is a moot point. Has anybody managed to resample and the beating remain?

At 96kHz sampling rate the filter effects at 20kHz are somewhat different than when sampling at 44.1kHz. This is a measurable result but whether or not many, or any, people can truly hear it does not seem to have been established by impartial studies.

MOST audio players (as part of the DAC) use anti-alaising filters. The image is reflected back down from the Nyquist limit. That means it gets mixed into the music.

No. This is the case in an ADC. In a DAC, it is the opposite, it's the content below the Nyquist frequency that is reflected above the Nyquist limit. They are the ultrasonic harmonics that create the rectangle steps if the output is unfiltered.Anyway, since CD are recorded with anti-alias filters, there is nothing left above 22050 Hz that could be "reflected back" in a DAC.

QUOTE (Hollunder @ Feb 6 2006, 04:53 PM)

So if I'm right a Anti-alias Filter is a low-pass filter (lets signals below a certain frequency go through) that cuts off every frequenzy above half the sample frequency to avoid alias-signals.

The Problem is that those filters can't be "perfect" but if you apply them at a higher sampling-frequency the result will be closer to perfect

They can be perfect in practice, but we don't want them to be perfect. It would cause a lot of oscillations at 22050 Hz. It could cause distortions and even endager the tweeters.

QUOTE (hdante @ Feb 7 2006, 11:27 PM)

Mathematically, cos(32KHz)+cos(30KHz) = 2*cos(31KHz)*cos(1KHz). Add the time in equation and you have a 1 KHz harmonic with a variable intensity of 2*cos(31KHz*t).

Mathematically, a 32 kHz frequency is a trigonometric function of time, not of frequency !

Thus the sum of a 30 kHz and a 32 kHz sine is a 31 kHz sine that has a variable amplitude. This amplitude is given by the absolute value of Cos(1000 x 2 x Pi x t), that reach zero 2000 times per second, and 1 2000 times per second too.

QUOTE (mandel @ Feb 8 2006, 12:51 AM)

I just created a 96khz wav file with a 30k and a 32k tone and could hear a beat frequency as you say.

You cannot count 2000 beats in your head in one second ! What you hear is not a beat frequency, but a 2 kHz sinewave. It is one of the two intermodulation products of the 30 kHz and 32 kHz sinewaves, that are 2 kHz and 62 kHz (f2 - f1 and f2 + f1). This is called intermodulation distortion, or IMD. It occurs in amplifiers and speakers, as well as harmonic distortion, whose sum, Total Harmonic Distortion, is noted THD.

QUOTE (krabapple @ Feb 8 2006, 01:00 AM)

there's no silly idea that some audiophile won't embrace. There are belt-driven CD players out there too.

Here when mixing the 48 track recording down to stereo all in the digital domain there is a similar situation to the artificial one I created. Suppose that the first violins are playing a note with an overtone at 30khz and the second violins a note with a tone at 32khz, the close miking prevents the intermodulation distortion in the air from being recorded, however if all mixing is done at 96khz the distortion can reappear.

But who says that intermodulation occurs in the air ? It occurs in amplifiers, for sure ( http://world.std.com/~griesngr/intermod.ppt ). Nika Aldrich and I both ran an experiment where two tones are played in one speaker, 12 kHz and 18 khz, for example (18 kHz in inaudible for me). I could hear the 4 kHz intermodulation at loud volumes (play this more than half a second long and your tweeters are fried ! ). Then I played the 12 kHz in the left speaker, and the 18 kHz in the right one. I moved in several locations in the room in order to check that I was not standing at some anti-resonant nodes, but I could not hear the 4 kHz intermodulation anymore. Just the 12 kHz tone. Thus the intermodulation is stronger in the amplifier than in the air.If you play a high resolution recording, your amplifier will likely introduce more intermodulation than the air of the concert hall, and the result will be farther from the truth than a 44.1 kHz recording.

QUOTE (ChiGung @ Feb 9 2006, 03:53 AM)

The question of how this beat period is generating an actual tone (...) on playback of the record, is in contention in this thread.

Let's consider the example of an amplifier. Say that its voltage gain is 3.00 when no signal passes though it. Input 1.00 milliVolt, it outputs 3.00 milliVolts.This won't be true when the amplifier is driven at high powers. When the output voltage rises, it slowly goes towards the clipping limit. The ascention is not perfectly linear. For example, if you input 1 Volt, it might output 2.99 Volts instead of 3 Volts. The Voltage gain is no more 3.00, but 2.99.This will cause a periodic deformation of the additional signals fed into the amplifier.When you feed 30 kHz into this amplifier, its gain will be 3.00 60000 times each second, but it will fall to 2.99 60000 times per second. The 32 kHz sine that you then add won't benefit from a constant gain, but from a variable gain that oscillates between 2.99 and 3.00 60000 times per second. This is the cause of the apparition of a real 2 kHz sinewave, that should not exist in a perfect amplifier.

QUOTE (ChiGung @ Feb 9 2006, 03:53 AM)

Some believe that the beat period will be heard as a tone (walkers pace), or that the period will produced a tone in the air ~maybe a fluid dynamic phenomenon or something.

According to David Griesinger's study, the amplifier is the main culprit. He did not measure significant amounts of intermodulation distortion in the tested tweeters.We should however expect a lot of IMD in woofers, since their response will be drastically reduced when their diaphragm moves far from its resting position.But David Griesinger's measurments were made 15 cm away from the tweeter. Thus we can't tell from these data if the intermodulation in significant through, say, 15 meters of air. All we can say is that it will depend on the sound pressure level. Intermodulation will appear when the sound compresses the air enough for its acoustic properties to be affected. Like it appears in the amplifier when the voltage is high enough to affect its gain.

QUOTE (ChiGung @ Feb 9 2006, 03:53 AM)

When the ultrasonic test signal is lowpassed to remove theoreticaly inaudible frequencies from the record, the 'sound' of the beat frequency disappears as well.

...unless it has suffered from intermodulation before the lowpass. Then a real 2 kHz sinewave have appeared, and is still there after the lowpass.

QUOTE (Hollunder @ Feb 9 2006, 05:26 AM)

I guess the best way to proof that it has influence on the realworld-sound is to produce such a signal in the realworld. If we can't it's not a proof that it's impossible, but if we can...

What would be needed to do so?

A microphone and a mic amplifier more linear than air

QUOTE (bug80 @ Feb 9 2006, 08:51 PM)

And how exactly did you do that? If you add two tones of 440 Hz and 450 Hz you should not end up with a 445 Hz tone, since addition is linear. You should hear a superposition of both tones (you should hear them both at once), plus a beating effect, which is again just a temporal change in amplitude, not in frequency.

In english : the sum of a 440 Hz sine and 450 sine is a 445 Hz sine whose amplitude reaches zero 10 times per second.

This is the same deal as joint stereo versus stereo. You can write it Left + Right, or Mid + Side, this is exactly the same signal. Just two ways of writing it.Here, you can write 440 Hz and 450 Hz, or 445 Hz variating, this is exactly the same signal. Two ways of writing it. You can hear the frequencies together or separately, like you can hear an instrument note as a whole, or listen to its harmonics separately.

So you really get a 445 Hz oscillation. But you cannot say that its frequency is 445 Hz, because by definition, a frequency is a signal whose amplitude never changes. Its spectrum is made from 440 Hz and 450 Hz components. Filter it at 445 Hz, and only the 440 Hz part remains, without the beating.

Another way of seeing it would be a 10 Hz signal whose fundamental's amplitude is completely null. The second harmonic is silent too. So are the next harmonics... Only the 44th and 45th harmonics are not silent.

Personally don't like the idea of high amplitude ultrasonic sound being shot at me without plenty of medical research showing that high SPL ultrasound really is harmless and that it won't cause someone's hearing aid to burst into flame or explode.

As for sampling rates, 44.1 kHz's fine with me since a decent microphone should record anything that my ear would if it were in the same general location and I most definately can't hear beyond 20 kHz (and that's being generous. )

And how exactly did you do that? If you add two tones of 440 Hz and 450 Hz you should not end up with a 445 Hz tone, since addition is linear. You should hear a superposition of both tones (you should hear them both at once), plus a beating effect, which is again just a temporal change in amplitude, not in frequency.

Wrong.

QUOTE

So you really get a 445 Hz oscillation. But you cannot say that its frequency is 445 Hz, because by definition, a frequency is a signal whose amplitude never changes. Its spectrum is made from 440 Hz and 450 Hz components.

How can you first say I'm wrong and then say exactly the same thing as I did in other words

Anyway, it really depends on how far the tones are apart in the frequency domain. If you add two tones of 200 and 2000 Hz you don't really hear a 1100 Hz tone beating. For 440 Hz and 450 Hz I really hear two seperate tones and for 445 Hz and 450 Hz I don't anymore.

Anyway, it really depends on how far the tones are apart in the frequency domain. If you add two tones of 200 and 2000 Hz you don't really hear a 1100 Hz tone beating. For 440 Hz and 450 Hz I really hear two seperate tones and for 445 Hz and 450 Hz I don't anymore.

Just to clarify something real quick here...

The beat frequency is the difference or the addition of the other two frequencies. For 2000 and 200, the beat freqs will be 1800 and 2200. In the other example that has been presented, with 30k and 32k, 2k is indeed the correct beat frequency (not 1k as someone expected) with another beat frequency at 62k.

If a signal mixer is being used, then you also get those real freqs, plus all of their sums and differences, plus all of their harmonics. These complications are why radio devices interfere with each other, even if they are in completly different frequency ranges.